An Integrability Theorem for Almost-Kähler Structures using J-anti-invariant Two-Forms on Four-Manifolds

Abstract

We establish a new criterion for a compatible almost complex structure on a symplectic four-manifold to be integrable and hence Kähler. Our main theorem shows that the existence of three linearly independent closed J-anti-invariant two-forms implies the integrability of the almost complex structure. This proves the conjecture of Draghici-Li-Zhang in the almost-Kähler case

This paper has been withdrawn due to a crucial sign error in the proof of Proposition 14. The authors are very thankful to Tedi Draghici for kindly pointing it out